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Home , Foe (unit), Iron group, Nucleosynthesis, Photodisintegration

Lecture 15

Explosive and the r-Process As the shock wave passes through the , matter is briefly heated to temperatures far above what it would have experienced in hydrostatic equilibrium. This material expands, then cools nearly adiabatically (if the input from shock heating exceeds that from nuclear burning). The time scale for the cooling is approximately the hydrodynamic time scale, though a little shorter. For (post-) burning in hydrostatic equilibrium, recall

ε ≈ ε nuc ν hydrostatic nucleosynthesis advanced stages of For explosive nucleosynthesis :

τ nuc (Tshock ) ≤ τ HD

ρ ∝ T 3 ρ(t) = ρshock exp(−t / τ HD ) 9 −3/ 4 T(t) = Tshock exp(−t / 3τ HD ) Tshock ≈ 2.4 x10 R9

446 sec ρshock ≈ 2 ρo τ HD = ρ shock Except near the "mass cut", the shock temperature to which the explosive nucleosynthesis is most sensitive is given very well by 4 π R3 aT 4 ≈ Explosion energy 3 ≈ 1051 erg Example:

Any present inside of 109 cm will burn explosively if:

0.1 HD Conditions for explosive burning (E0 = 1.2 B):

To nse T9 >5 R9 < 0.38 yes Silicon 4 − 5 0.38 − 0.51 yes 3 − 4 0.51 − 0.74 yes 2.5 −3 0.74−1.0 a little Carbon 2.0 − 2.5 1.0−1.3 no Helium >0.5 < 8 no Hydrogen >0.2 < 27 no

−4/3 ⎛ T ⎞ Roughly speaking, everything that is R = 9 9 ⎜ 2.4 ⎟ ejected from inside 3800 km in the ⎝ ⎠ presupernova star will come out as - elements.

Ni O Si ESiB

EOB

ENeB

Ejected without much modification Produced pre-explosively and just ejected in the :

• Helium • Carbon, nitrogen, oxygen • The s-process • Most species lighter than

Produced in the explosion: • Iron and most of the elements – Ti, V, Cr, Mn, Fe Co, Ni • The r-process (?) • The neutrino process – F, B

Produced both before and during the explosion: • The intermediate mass elements – Si, S, Ar, Ca • The p-process (in oxygen burning and explosive Ne burning)

25 Solar Masses; Rauscher et al. (2002) The amount of iron group synthesis (56Ni) will depend sensitively upon the density distribution around the collapsed core. Higher mass will synthesize more iron. The nucleosynthesis that results from explosive silicon burning is sensitive to the density (and time scale) of the explosion.

1) High density (or low entropy) NSE, and long time scale:

Either the material is never photodisintegrated even partially to particles or else the -particles have time to reassemble into iron-group nuclei. The critical (slowest) reaction rate governing the reassembly is (2,)12C which occurs at a rate proportional to 2.

If as T →0, Xn , X p , and Xα →0 then one gets pretty much the unmodified "normal" results of nuclear statistical equilibrium calculated

e.g.,at T9 = 3 (fairly indedendent of ρ).

Abundant at η= 0.002 − 0,004 56,57Ni, 55Co, 52,53,54Fe, 48,49,50Cr, 51 Mn Products: 54,56 55 48,49 50,51,52,53 51 Fe, Mn, Ti, Cr, V 2) Low density or rapid expansion à the “-rich” freeze out

If all the α's cannot reassemble on τ HD , then the composition will be moditied at late times by α-capture. The composition will "freeze out" with free α-particles still present (and, in extreme cases, free n's or p's). The NSE composition at low T willbe modified by reactions like

54 Fe(α,γ )58 Ni 56 Ni(α, p)59 Cu 56 Ni(α,γ )60 Zn 40Ca(α,γ )44Ti 57 Ni(α,γ )61 Zn 58 Ni(α,γ )62 Zn etc.

Abundant: 44Ti, 56,57,58Ni, 59Cu, 60,61,62Zn,(64,66Ge) Produced : 44Ca, 56,57Fe, 58,60,61,62 Ni, 59Co,(64,66Zn)

3) Explosive oxygen burning (3 ≤ T9 ≤ 4) Makes pretty much the same products as ordinary oxygen

burning (T9 ≈ 2) at low η ≈0.002 (Z/Z ) Principal Products: 28Si, 32,33,34S, 35,37Cl, 36,38Ar 39,41K, 40,42Ca, 46Ti, 50Cr

4) Explosive neon burning (2.5≤T9 ≤3.0) Same products as stable hydrostatic neon buring More 26Al, the p-process or γ -process.

5) Explosive H and explosive He burning. The former occurs in novae; the latter in some varieties of Type Ia supernovae. Discuss later. The “p -” or

 - Process

At temperatures ~2 x 109 K before the explosion (oxygen burning) or between 2 and 3.2 x 109 K during the explosion (explosive neon and oxygen burning) partial of pre-existing s-process seed makes the -rich elements above the iron group. The p-Process (aka the -process) p-nuclei

A 25 M Supernova

Problems below A ~ 130. Summary: Process

• Makes nuclei traditionally attributed to the “p-process” by photodisintegration of pre-existing s-process nuclei. The abundance of these seeds is enhanced – at least for A < 90 – by the s-process that went on in He and C burning.

• Partially produced in oxygen shell burning before the collapse of the iron core, but mostly made explosively in the neon and oxygen- rich shells that experience shock temperatures between 2 and 3.2 billion K.

• Production factor ~100 in about 1 solar mass of ejecta. Enough to make solar abundances

• A secondary (or tertiary) process. Yield is proportional to abundance of s-process in the star.

• There remain problems in producing sufficient quantities of p-nuclei with atomic masses between about 90 and 120, especially 92Mo. The Neutrino Process (-process)

The neutrino flux from star formation in the center can induce in the overlying layers of ejecta. The reactions chiefly involve µ and -neutrinos and neutral current interactions. Notable products are 11B, 19F. 138La, 180Ta, and some 7Li and 26Al.

Production factor relative to solar normalized to 16O production as a function of µ and τ neutrino temperature (neutral current) and using 4 MeV for the (anti-)neutrinos (for charged current only).

Product

6 MeV 8 MeV 6 MeV 8 MeV

This This WW95 WW95 This work WW95 This work WW95 work work

11B 1.65 1.88 3.26 3.99 0.95 1.18 1.36 1.85

19F 0.83 0.60 1.28 0.80 0.56 0.32 1.03 0.53

15N 0.46 0.49 0.54 0.58 0.09 0.12 0.15 0.19

138La 0.97 1.10 0.90 1.03

180Ta 2.75 3.07 4.24 5.25

Heger et al,, 2005, Phys Lettr B, 606, 258 Integrated Ejecta

Averaged yields of many supernovae integrated either over an IMF or a model for galactic chemical evolution. Survey - Solar : (Woosley and Heger 2007) • Composition – Lodders (2003); Asplund, Grevesse, & Sauval (2004)

• 32 stars of mass 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 35, 40, 45, 50, 55, 60, 70, 80, 100, 120 solar masses. More to follow.

• Evolved from main sequence through explosion with two choices of mass cut (S/NAkT = 4 and Fe-core) and two explosion (1.2 foe, 2.4 foe) – 128 supernova models

• Averaged over Salpeter IMF Woosley and Heger, Reports, 442, 269 - 283, (2007) Isotopic yields for 31 stars averaged over a Salpeter IMF,  = -1.35

Intermediate mass elements (23< A < 60) and s-process (A = 60 – 90) well produced.

Carbon and Oxygen over- produced. p-process deficient by a factor of ~4 for A > 130 and absent for A < 130 Survey

Z = 0; 10 to 100 M (Heger & Woosley, 2010, ApJ, 724, 341)

Big Bang initial composition, Fields (2002), 75% H, 25% He

10−12M ΔM = 0.1M

12−17 M ΔM = 0.2 M Evolved from main sequence to 17 - 19 M ΔM = 0.1 M   presupernova and then exploded 19− 20 M ΔM = 0.2 M with pistons near the edge of the iron core (S/N k = 4.0) 20 - 35 M ΔM = 0.5 M A

35 - 50 M ΔM = 1 M

50 - 100 M ΔM = 5 M Each model exploded with a variety of energies from 0.3 to 126 Models 10 x 1051 erg. at least 1000 supernovae “Standard model”, 1.2 B,  = 1.35, mix = 0.1, 10 - 100 solar masses Best fit, 0.9 B,  = 1.35, mix = 0.0158, 10 - 100 solar masses Lai et al. 2008, ApJ, 681, 1524

28 poor stars in the Milky Way Galaxy -4 < [Fe/H] < -2; 13 are < -.26

Eexp Cr I and II, non-LTE effects; see also KE = Eo (20/M) B Sobeck et al (2007) mixing 0.1 would have been "normal" and now 17O

Woosley, Heger, & Weaver (2002) The r-Process

The rapid addition of to iron group nuclei that produces the most neutron-rich up to and beyond. This is though to occur either in the deepest ejecta of supernovae or in merging neutron stars. The r-Process The r-Process The r-process path hits the closed neutron shells for a smaller value of A (i.e., a lower Z) These heavy nuclei cannot be made by the s-process, nor can they be made by charged particle capture or photodisintegration.

Photodisintegration would destroy them and make p-nuclei. The temperatures required for charged particle capture would destroy them by photodisintegration.

Their very existence is the proof of the addition of neutrons on a rapid, explosive time scale. This requires a high density of neutrons.

They were once attributed to the , but the density is far too low.

Still, observations suggest though that the r-process arose or at least began to be produced very early in the universe, long before the s-process. The r-process is “primary”

Truran, Cowan, and Field (2001) If neutrons are to produce the r-process nuclei then -decay must be responsible for the increase in proton number along the r-process path. would combine with neutrons and end up in helium. (neutrino capture? fluxes probably too small)

The neutron density must be high both because the abundances themselves indicate a path that is very neutron-rich (so  Yn n must be >> 1/ near the valley of -stability) and because only very neutron-rich nuclei have sufficiently short -decay lifetimes to decay and reach, e.g., Uranium, before Yn goes away (HD) in any realistic scenario. The lifetimes of nuclei that are neutron-rich become increasingly short because of the large Q-value for decay: • More states to make transitions to. Greater liklihood that some of them have favorable spins and parities

• Phase space – the lifetime goes roughly as the available energy to the fifth power

We shall find that the typical time for the total r-process is just a few . Neutron rich nuclei have smaller

cross sections because Qng decreases, eventually approaching zero Take λ  104. One needs ρ Y λ >> 1. t < 1 s ⇒ nγ n nγ for many captures to happen in a N A 20 -3 This implies that n = ρ N Y >> ~ 10 cm 1 ⎛ dYA ⎞ n A n = ρY λ λ ⎝⎜ ⎠⎟ n nγ nγ YA dt For such large neutron densities neutron capture will go to the (T-dependent) neutron drip line and await a beta decay. How it works The r-process proceeds by rapidly capturing neutrons while keeping Z constant, until a "waiting point" is reached. At the waiting point(s), photo-neutron ejection (photodisintegration) balances neutron capture. At zero temperature, the waiting point would be the neutron drip line (Sn ≤0), but the r-process actually happens at high temperature (a necessary condition to obtain the high neutron density).

At the waiting point (or points), beta decay eventually happens creating Z+1. Neutron capture continues for that new element until a new waiting point is found.

 

Qng small or negative •→•→••→•• from here onwards even odd even odd (high) (low) (high) (very low) abundance

Y λ ( A+1) = ρ Y Y λ ( A) A+1 γ n n A nγ The temperature cannot be too high or

• The heavy isotopes will be destroyed by photo- disintegration

• (,n) will balance (n,) too close to the valley of

 stability where  is long

At a waiting point for a given Z: λ ( A) A + n A + 1 YA+1 nγ = ρ Yn γ YA λγ n ( A+1) −1 G( A+1) ( A+1) = ρ Y 9.89 × 109 T −3/2 exp(11.6045Q / T ) n ( ) 9 nγ 9 G( A) A

At a waiting point photodisintegration will give YA+1 and YA comparable abundances – at least compared with abundances far from A. Since we only care about log’s anyway … Ignoring G’s and other less dominant terms

YA+1 log  0  log ρYn −10 + 5.04Qnγ /T9 YA

 Yn T9 Qlim(MeV)

1 gm cm-3 1 1.98 2 3.97 3 5.94

103 gm cm-3 1 1.39 2 2.78 3 4.17

Therefore the path of the r-process (Qlim) depends upon a combination of T9 and nn. Actually both are functions of the time. Optimal conditions for the r-process

Based upon estimated lifetimes and Q-values along path of the r-process.

Kratz et al. (1988)

For example, at T9=2.5, 27 -3 nn = NAYn ~ 10 cm 3 or Yn ~ 10 . Sites for the r-process:

All modern scenarios for making the r-process achieve a very large density of neutrons and a very high neutron-to- seed ratio by invoking an explosive event in which the matter is, at least briefly, in the form of – neutrons and protons – with a large excess of neutrons. The ensuing nucleosynthesis then resembles a dense, neutron-rich Big Bang.

Many n + some p → Some 4He + many neutrons 4 → Heavy elements + He + many neutrons

This last step would not happen at Big Bang densities but happens in a stellar environment where the density is enormously greater. Three sites are currently discussed:

• Neutrino-powered winds from proto-neutron stars

• Merging neutron stars and neutron stars merging with black holes

• Dense accretion disks around black holes could be an outcome of merging neutron stars) r-Process Site #1: The Neutrino-powered Wind *

Anti-neutrinos are "hotter" than the neutrinos, thus weak equilibrium implies an appreciable neutron excess, typically 60% neutrons, 40% protons

* favored

T9 = 5 – 10

T9 = 3 - 5

T9 = 1 - 2

e.g., 5% by mass “Fe” and 20% by mass neutrons

(Ye = 0.4) implies 200 neutrons per iron. The other 75% is alphas. Nucleonic wind, 1 - 10 seconds

Duncan, Shapiro, & Wasserman (1986), ApJ, 309, 141 Woosley et al. (1994), ApJ, 433, 229 Mass loss rate – neutrino driven wind – post SN

After 0.1 s, the luminosities of all flavors of neutrinos are equal - made by pair annihilation But the average energy each flavor of neutrino is not the same In order for this to work one needs.

1) low Y because T > T e νe νe

T3 2) High entropy S ~ (entropy dominated by radiation) ρ need S~ 400 If the density is too high, too many alphas reassemble For higher entropy the density is lower at and the neutron to seed ratio a given temperature. The rates governing the is small reassembly of α-particles are proprtional to ρ 2 (the 3α reaction) or ρ3 (the ααn reaction)

R 3) Rapid time scale - τ ~ ~ 100ms. v wind

Why it hasn’t worked so far

Need entropies srad/NAk ~ 400. Most calculations give ~ 100. Magnetic fields could help – Thompson 2003, ApJL, 585, L33. Neutrino-powered wind

Roberts, Woosley and Hoffman (2010) r=Process Site #2 - Merging Neutron Stars

May happen roughly once every 107 years in the Milky Way galaxy. Eject up to 0.1 solar masses of r-process.

May be too infrequent to explain r-process abundances in very metal deficient stars (Argast et al, 2004, A&A, 416, 997).

Nevertheless, probably the currently favored site. Rosswog et al. 2003, MNRAS, 345, 1077 and references therein

May also jet of neutron rich material after merger Burrows et al., 2007, ApJ, 664, 416 Merging neutron stars – r-process nucleosynthesis Goriely, Bauswein, and Janka (2011)

5000 network up to Z = 110; Postprocessing 3D SPH calculation of the 0.001 to 0.01 M ejected  merger −5 −1 merger rate 10 yr

So many neutrons that “fission recycling” occurs leading to a robust pattern that fits the solar abundances above A = 110. Also need a “weak” r-process site. Wanajo and Janka (2012)

Neutrino-powered wind from following merger “” Kasen et al MNRAS (2015)

model is characterized by time in ms before a BH forms